Russian Physics Journal

, Volume 49, Issue 4, pp 364–378 | Cite as

Two regularization types as two different Nambu-Iona-Lasinio models

  • R. G. Jafarov
  • V. E. Rochev
Article

Abstract

The Nambu-Iona-Lasinio models with 4-dimensional cutting and dimensional-analytical regularization types are compared. It is demonstrated that they describe two different models of light quark interaction. In the average-field approximation, the behavior of the scalar amplitude differs in the threshold region. Unlike the 4-dimensional cutting regularization in which the pole term corresponding to a sigma-meson can be separated near the threshold, the singularity of the scalar amplitude in the dimensional-analytical regularization is non-pole; moreover, it disappears completely for a certain value of the regularization parameter. One more significant difference between the two models is in the first-order expansion of the average field. The calculated meson contributions to the quark chiral condensate and dynamic quark mass demonstrate that despite their relative smallness, they can destabilize the Nambu-Iona-Lasinio model with 4-dimensional cutting regularization. On the contrary, the model with dimensional-analytical regularization is stabilized, which is manifested through a shift of regularization parameter values toward the stability region in which the contributions themselves decrease.

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References

  1. 1.
    Y. Nambu and G. Jona-Lasinio, Phys. Rev., 122, 345 (1961).CrossRefADSGoogle Scholar
  2. 2.
    T. Eguchi and H. Sugawara, Phys. Rev., D10, 4257 (1974); K. Kikkawa, Prog. Theor. Phys., 56, 947 (1976); H. Kleinert, Understanding the Fundamental Constituents of Matter, A. Zichichi, ed., Plenum Press, New York (1978); D. Ebert and M. K. Volkov, Z. Phys., C16, 305 (1983).ADSGoogle Scholar
  3. 3.
    S. P. Klevansky, Rev. Mod. Phys., 64, 649 (1992).MathSciNetCrossRefADSGoogle Scholar
  4. 4.
    T. Hatsuda and T. Kunihiro, Phys. Rep., 247, 221 (1994).CrossRefADSGoogle Scholar
  5. 5.
    E. N. Nikolov et al., Nucl. Phys., A608, 411 (1996).ADSGoogle Scholar
  6. 6.
    E. Quack and S. P. Klevansky, Phys. Rev., C49, 3283 (1994); D. Ebert, M. Nagy, and M. K. Volkov, Yad. Fiz., 59, 149 (1996).ADSGoogle Scholar
  7. 7.
    M. Oertel, M. Buballa, and J. Wambach, Nucl. Phys., A676, 247 (2000).ADSGoogle Scholar
  8. 8.
    S. Krewald and K. Nakayama, Ann. Phys., 216, 201 (1992).MATHMathSciNetCrossRefADSGoogle Scholar
  9. 9.
    R. G. Jafarov and V. E. Rochev, Centr. Eur. J. Phys., No. 2, 367 (2004) [hep-ph/0311339].Google Scholar
  10. 10.
    W. Ochs, Plenary talk at “Hadron 03” (Aschaffenburg, Germany) [hep-ph/031144].Google Scholar
  11. 11.
    H. Kleinert and B. Van der Bossche, Phys. Lett., B474, 336 (2000).ADSGoogle Scholar
  12. 12.
    E. Babayev, Phys. Rev., D62, 074020 (2000); G. Ripka, Nucl. Phys., A683, 463 (2001).Google Scholar
  13. 13.
    V. E. Rochev, J. Phys., A30, 3671 (1997); V. E. Rochev and P. A. Saponov, Int. J. Mod. Phys., A13, 3649 (1998); V. E. Rochev, J. Phys., A33, 7379 (2000).MathSciNetADSGoogle Scholar
  14. 14.
    V. E. Rochev, Talk given at the 17th International Workshop on High-Energy Physics and Quantum Field Theory (QFTHEP’2003), Samara-Saratov (2003) [hep-ph/0312004].Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • R. G. Jafarov
    • 1
  • V. E. Rochev
    • 1
  1. 1.Baku State UniversityRussia

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